Atomic Energies from ONETEP

ONETEP [1], the order-N electronic total energy package is a numerical implementation of Density Functional Theory. Unlike usual implementations of DFT, the computational resources required for the calculation of the energy of a particular atomic system scales linearly with the number of electrons, which makes it exceptionally efficient in investigations of large systems. However, in our work we exploited another feature of ONETEP, namely, that it uses local basis functions. 

The electronic structure of periodic crystalline solids is usually represented by Bloch orbitals where n and k are quantum numbers of the band and crystal momentum, respectively. The Bloch states are eigenfunctions of the Hamiltonian of the crystal, obeying the same periodicity. Because of the fact that they are usually highly delocalised, it is often difficult to deduce local properties from Bloch orbitals, for instance, bonding between atoms or atomic charges. 

An equivalent representation of the electronic structure is provided by Wannier functions [2], which are connected to the Bloch orbitals via a unitary transformation. Denoting the Wannier functions of band n of cell R by Wn v — R), we express the transformation as follows  

The Wannier functions obtained in Eq. 6.25 are not unique, because it is possible to mix the Bloch states of different band numbers by a unitary matrix The resulting Wannier functions are also a complete representation of the electronic structure, although their localisation features are different  

Since both transformations in 6.25 and 6.26 are unitary, and the original Bloch states are orthogonal, the resulting Wannier functions are also orthogonal. 

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As a test system, we used clusters of 29-71 silicon atoms. The configurations were generated by molecular dynamics simulation at 3,000 K, where the forces were obtained from the StiUinger—Weber potential [4]. We performed the electronic structure calculations of the different clusters using ONETEP, and we also used ONETEP to determine the atomic energies, as described in Sect. 6.1.2. A typical cluster is shown in Fig. 6.1. 

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